 Hi, I'm Zor. Welcome to Unizor Education. I will just present a very simple problem related to angles. It's a very short one and really very, very simple one. But it's just an introduction into a series of problems which might actually be much more complex than this. In any case, we always start with the simple thing and then we go to more complex. So here's the problem. Let's consider we have two supplementary angles. Supplementary means that together they form 180 degree angle. So this is my angle alpha and this is my angle 180 degrees minus alpha. So the problem is let's have two bisectors of these two angles. Bisector of this angle and bisector of supplementary angle. One angle will be A, O, B. Another will be B, O, C. And the bisectors they will call G and E. So what's given? Given that A, O, B and B, O, C are together 180 degrees. Okay, angle A, O, B plus angle of B, O, C equals 180 degrees. Now when I have angle plus angle it actually means measure of this angle. So excuse me if I don't put this measure off or something. What else is given? That O, G is bisecting the angle A, O, B, which means angle A, O, G. A, O, G is congruent to G, O, B. And this bisector is dividing the B, O, C in half. So the angle B, O, E is congruent to E, O, C. Okay, what should be proven? We're to prove that angle D, O, E, the one which is composed of two bisectors, measure of this angle is 90 degrees. So these are perpendicular to each other. Well, I spent so much time explaining the condition basically of this little problem. Solution is absolutely trivial. Let's think about it in the following way. The angle D, O, E, the one which we have to really calculate the value of, it's a sum of two angles, G, O, E and D, O, E. D, O, B plus B, O, E, which in turn equal to, if this angle measures as alpha, and this measures as 180 degree minus alpha. So half of this, since O, D is bisecting, so half of this will be one half of alpha plus one half of 180 degree minus alpha, which is equal to, well, if you will open this parenthesis, you will have one half alpha plus one half of 180, which is 90 degree, and minus one half alpha, which is equal to 90 degree. So that's the proof. Very easy. And I don't want you to be very excited about this particular problem if you solve it yourself. There is absolutely nothing to it. It's a very easy one. But anyway, as I was saying, it's always the simple problems which will fade the road to more complex ones. So thanks very much, and good luck in other problems.